Question

A Department of Transportation (DOT) official is investigating the possibility of collusive bidding among the state’s road construction contractors. One aspect of the investigation involves a comparison of the winning (lowest) bid price y on a job with the length x of new road construction, a measure of job size.(Using SPSS program)

Data: X Y

2.00   10.10
2.40   11.40
3.10   24.20
3.10   26.50
6.40   66.80
6.10   53.80
7.00   71.10
11.50   132.70
10.90   108.00
12.20   126.20
12.60   140.70

a) Use the method of least squares to obtain the estimated regression function.

b) Conduct a formal test for the lack of fit?

c) At 10% level of significance test if there is any autocorrelation

d) Test the normality assumption at 10% significance level.

e) At 10%, level of significance test if the error variance is constant. State the alternatives, decision rule, and conclusion.

f) Use the transformation Y’ = ln (Y) then obtain the estimated linear regression for the transformed data.

g) Express the estimated regression function in the original units

h) Obtain the residuals and plot them against the fitted values. Also, prepare a normal probability plot. What do your plots show?

i) Estimate the standard deviation function by regressing the absolute values of the residuals against x, and then calculate the estimated weight.

j) Carry out the weighted least squares estimates of β0 and β1 using the weights determined in part (j).

k) Are the weighted least squares estimates for similar to the ones obtained with ordinary least squares in part (b)?

l) Compare the estimated standard deviations of the weighted least squares estimates β0 and β1in part (k) with those for the ordinary least squares estimates in part (b). What do you find?

Answer 1